Patient who weighs more than the weight limit for the PET table Patients must have undergone radical hysterectomy (open, laparoscopically or robotic) and staging including pelvic node sampling or dissection for cervical carcinoma within 70 days prior to study entry (NOTE: if the patient did not have a para-aortic lymph node sampling/dissection, but had common iliac node dissection that was negative, a positron emission tomography [PET]-computed tomography [CT] is recommended, but not required; a negative pre or post-operative PET scan or PET-CT scan of the paraaortic nodes is required if the patient did not undergo para-aortic or common iliac nodal sampling/dissection) Patients with clinical stage IA2, IB or IIA squamous, adenosquamous, or adenocarcinoma of the cervix who have any/all of the following high-risk features after surgery:* Positive pelvic nodes* Positive parametrium* Positive para-aortic nodes- completely resected, PET/CT negative (PET only required if positive para-aortic nodes during surgery) No distant metastases, based upon the following minimum diagnostic workup (NOTE: patients with positive para-aortic nodes- completely resected, PET/CT negative are eligible):* History/physical examination within 56 days prior to study entry* Contrast-enhanced imaging of the abdomen and pelvis by either CT, magnetic resonance imaging (MRI), or whole body PET-CT (with or without contrast) within 90 days prior to registration (NOTE: whole body PET-CT is preferred) * Chest x-ray (posterioranterior [PA] and lateral) or chest CT within 70 days prior to study entry (except for those who have had whole body PET-CT) Patients may have had one cycle only of ABVD prior to enrolling on study; no other prior treatment (chemotherapy or radiation therapy) for Hodgkin lymphoma is allowed; if patient has had one cycle of ABVD, in order to be eligible to enroll on Cancer and Leukemia Group B (CALGB) 50801, the patient must have had all of the following tests prior to starting the first cycle of ABVD:* Left ventricular ejection fraction (LVEF) by echocardiogram (ECHO) or multi gated acquisition (MUGA)* Pulmonary function tests (PFTs) (including diffusing capacity of the lung for carbon monoxide [DLCO]/forced vital capacity [FVC])* CT scan (neck**, chest, abdomen, pelvis)* FDG-PET/CT scan* Chest X-ray, posterior-anterior (PA) & lateral* Complete blood count (CBC), differential, platelets* Erythrocyte sedimentation rate (ESR)* Serum creatinine* Glucose* Aspartate aminotransferase (AST)* Alkaline phosphatase* Bilirubin* Lactate dehydrogenase (LDH)** Patients with a negative FDG-PET/CT scan do not need to have had a dedicated neck CT scan prior to starting the previous cycle of ABVD Patients must have a diagnostic quality contrast-enhanced CT scan of the chest, abdomen, and pelvis AND baseline FDG-PET scan performed within 28 days prior to registration* Low-resolution localization CT scans performed as part of a combined PET/CT scan are not adequate for enrollment or response determination on this protocol* If a patient has an allergy to CT contrast, then a non-enhanced CT will be acceptable Interim PET/CT scans must have been submitted for centralized review No evidence of bone metastases (M0) on bone scan within 120 days prior to registration (sodium fluoride [NaF] positron emission tomography [PET]/CT is an acceptable substitute)* Equivocal bone scan findings are allowed if plain films (or CT or magnetic resonance imaging [MRI]) are negative for metastasis Patients must have at least ONE of the following:* Measurable tumor on magnetic resonance imaging (MRI), computed tomography (CT) scan obtained within 3 weeks prior to study entry; measurable is defined as >= 10 mm in at least one dimension on spiral/helical CT that is metaiodobenzylguanidine (MIBG) avid or demonstrates increased fludeoxyglucose (FDG) uptake on positron emission tomography (PET) scan* MIBG scan obtained within 3 weeks prior to study entry with positive uptake at a minimum of one site; this site must represent disease recurrence after completion of therapy, progressive disease on therapy, or refractory disease during induction* Patients with resistant/refractory soft tissue disease that is not MIBG avid or does not demonstrate increased FDG uptake on PET scan must undergo biopsy to document the presence of viable neuroblastoma; biopsy is not required for patients who have new site of soft tissue disease (radiographic evidence of disease progression) regardless of whether progression occurs while receiving therapy or after completion of therapy* Note: Patients with elevated catecholamines (i.e., > 2 x ULN) only or bone marrow disease only are NOT eligible for this study Patient must have clinically T1-3, N1 breast cancer at the time of diagnosis (before neoadjuvant therapy); clinical axillary nodal involvement can be assessed by palpation, ultrasound, CT scan, magnetic resonance imaging (MRI), positron emission tomography (PET) scan, or PET/CT scan Patients must have measurable disease; baseline measurements and evaluations must be obtained within 4 weeks of registration to the study; abnormal positron emission tomography (PET) scans will not constitute evaluable disease unless verified by a diagnostic quality computed tomography (CT) scan; patients must use the same imaging modality (CT or PET/CT) throughout the study RANDOMIZED PHASE II (ARMS K AND L): Patients must have measurable disease; baseline measurements and evaluations must be obtained within 4 weeks of registration to the study; abnormal PET scans will not constitute evaluable disease unless verified by a diagnostic quality CT scan; patients must use the same imaging modality (CT or PET/CT) throughout the study Stage II-IVB disease (American Joint Committee on Cancer [AJCC], 7th edition [ed.]) with no evidence of distant metastasis, based upon the following minimum diagnostic workup:* History/physical examination by a Medical Oncologist or Clinical Oncologist or Radiation Oncologist or Ear, Nose, Throat specialist (ENT), which must include an endoscopic evaluation, a complete list of current medications, and assessment of weight and weight loss in the past 6 months within 21 days prior to registration* Evaluation of tumor extent with one of the following combinations required within 28 days prior to registration:** Magnetic resonance imaging (MRI) of the nasopharynx and neck; or computed tomography (CT) of the nasopharynx and neck with =< 3 mm contiguous slices with contrast and bone windows (to evaluate base of skull involvement). ** MRI of the nasopharynx and positron emission tomography (PET)/CT (with contrast) of the neck*** Note: If a treatment planning CT scan is used, it must be with =< 3 mm contiguous slices with contrast and be read by a radiologist* To rule out distant metastasis, patients must undergo the following imaging within 28 days prior to registration:** A CT scan with contrast of the chest and abdomen (required), and the pelvis (optional), or a total body PET/CT scan (non-contrast PET/CT is acceptable)** A bone scan only when there is suspicion of bone metastases (a PET/CT scan can substitute for the bone scan) Evidence of metastatic breast cancer; patient considered at high risk of having disseminated disease (i.e. those with locally advanced disease, clinical N2-3 or pathological N1-3 with the exception of pN1a in adjuvant patients) should have a CT/MRI scan of the thorax/abdomen/pelvis or any other area as clinically indicated and a bone scan or a CT scan with bone windows at any point between diagnosis of the current breast cancer and randomization to rule out metastatic breast cancer; (note PET/CT scan may be used as an alternative imaging technique and precludes the need for bone scan); patients with screening ALT/AST or ALP above institutional upper limit of normal should have liver ultrasound, CT or MRI at any time point between diagnosis of current breast cancer and randomization; screening bone scan is required if ALP and/or corrected calcium level are above the institutional upper limit; (note PET CT scan may be used as an alternative imaging technique) Patients with alkaline phosphatase that is > ULN but =< 2.5 x ULN or unexplained bone pain are eligible for inclusion in the study if a bone scan, PET-CT scan, or PET scan performed within 90 days prior to randomization does not demonstrate metastatic disease No lytic lesions on skeletal survey and whole body positron emission tomography (PET)/computed tomography (CT) other than a single lesion associated with solitary bone plasmacytoma No lytic lesions on skeletal survey and whole body PET/CT other than a single lesion associated with solitary bone plasmacytoma within 28 days prior to registration Patients must be able to lie still for a 1.5 hour PET scan Patient must NOT weigh more than the maximum weight limit for the PET/CT table for the scanner(s) to be used at each center Patient must be able to lie still for a 20-30 minute PET/CT scan Patient must NOT weigh more than the maximum weight limit for the table for the PET/CT scanner at the institution where the study is being performed Patient has a new, unrated histologic diagnosis of stage IB2 (> 5 cm), II, IIIB or IVA squamous, adenocarcinoma, or adenosquamous carcinoma of the uterine cervix or stage II-IVA squamous, adenocarcinoma, or adenosquamous carcinoma of the vagina not amenable to curative surgical resection alone ; the presence or absence of para?aortic lymph node metastasis will be based on pre-therapy 18F?FDG PET/CT; if the baseline 18F?FDG PET/CT identifies hypermetabolic para?aortic disease, such patients will NOT be eligible; the patient must be able to tolerate imaging requirements of an 18F?FDG PET/CT scan Patients must have resectable primary tumor based on contrast-enhanced CT or MRI (CT or MRI without contrast as part of positron emission tomography [PET]/CT or PET/MRI is NOT acceptable; CT or MRI with contrast as part of PET/CT or PET/MRI is acceptable) of the chest, abdomen, and pelvis; the local interpreting radiologist must review the scans and sign the S1505 local radiology checklist prior to registration; resectable is defined as:* No involvement of the celiac artery, common hepatic artery, and superior mesenteric artery (and, if present, replaced right hepatic artery)* No involvement, or < 180 degrees interface between tumor and vessel wall, of the portal vein and/or superior mesenteric vein; and patent portal vein/splenic vein confluence* No evidence of metastatic disease; lymphadenopathy (defined as nodes measuring > 1 cm in short axis) outside the surgical basin (i.e., para-aortic, peri-caval, celiac axis, or distant nodes) is considered M1 disease and makes the patient ineligible; if, however, such nodes are biopsied and are negative, then enrollment can be considered after review with the study chairs* Note: for tumors of the body and tail of the pancreas, involvement of the splenic artery and vein of any degree is considered resectable disease Centers that standardly use positron emission tomography (PET) or magnetic resonance spectroscopy (MRS) to determine a diagnosis of radionecrosis are permitted to use these modalities to assist in their patient selection; however the criteria described for conventional MR and/or DSC should also be met for study eligibility; both PET and MRS are not mandatory for study eligibility Prior to chemotherapy +/- or thoracic radiotherapy, patients must be defined as limited-stage or extensive-stage SCLC after clinical staging evaluation involving the following:* History/physical examination;* Computed tomography (CT) of the chest and abdomen with contrast (does not have to be done if the patient has had a positron emission tomography (PET)/CT scan prior to initiating chemotherapy or thoracic radiotherapy)* MRI of the brain with contrast or diagnostic head CT with contrast* For patients without evidence of extensive-stage SCLC on chest and abdomen CT and brain MRI or head CT, a PET/CT or bone scan is required to confirm limited-stage SCLC After chemotherapy, patients must be restaged prior Step 1 registration using the same diagnostic work-up as required pre-chemotherapy; repeat PET/CT or bone scan is not required; patients must have:* History/physical examination within 30 days of Step 1 registration* No central nervous system (CNS) metastases (repeat MRI required) within 56 days prior to Step 1 registration* No progression in any site* Radiographic partial or complete response to chemotherapy in at least one disease site within 56 days prior to Step 1 registration** If PET/CT was obtained prior to chemotherapy, either a repeat PET/CT or CT of the chest and abdomen with contrast can be obtained for response assessment** Patients who underwent resection for limited-stage SCLC prior to chemotherapy and have no radiographically evident disease for response assessment remain eligible if post-chemotherapy imaging demonstrates no progression Patient must be able to tolerate imaging requirements of an 18-FDG-PET-CT scan Patients with hypermetabolic para-aortic disease identified on baseline 18-FDG-PET-CT Any pT-stage based on American Joint Committee on Cancer 7th edition eligible; study entry will be based on the following diagnostic workup:* History/physical examination within 60 days prior to step 1 registration* Negative distant metastatic workup: ** A computed tomography (CT) scan of the abdomen and pelvis (with contrast [CT without contrast is permitted if the patient is not a candidate for contrast, i.e., renal function or allergy]) or magnetic resonance imaging (MRI) of the pelvis within 120 days prior to step 1 registration; (Please note: Lymph nodes will be considered negative (NO)if they are =< 1.5 cm short axis);** Bone scan within 120 days prior to step 1 registration; (please note: a sodium fluoride [NaF] positron emission tomography [PET]/CT is an acceptable substitute and if the bone scan is suspicious, a plain x-ray, CT scan, NaF PET/CT and/or MRI must be obtained to rule out metastasis) No evidence of bone metastases (M0) on bone scan (Na F positron emission tomography (PET)/CT is an acceptable substitute) within 120 days prior to step 1 registration* Equivocal bone scan findings are allowed if plain films and/or MRI are negative for metastasis Patients must have follicular lymphoma (grade I, II or IIIa) confirmed at initial diagnosis and at relapse with identifiable fludeoxyglucose F-18 (FDG) avid disease on PET/CT; patients that have involvement with large cell lymphoma are not eligible Patients must have a whole body or limited whole body PET/CT scan performed within 42 days prior to registration